Solutions for a time-fractional diffusion equation with absorption: influence of different diffusion coefficients and external forces

This work is devoted to investigate explicit solutions of the time-fractional diffusion equations with external forces by considering various diffusion coefficients and an absorbent rate. Besides, the 2nth moment related to such an equation is also discussed. Consequently, the diffusion type can be determined from the mean-square displacement. In addition, a rich class of diffusive processes, including normal and anomalous ones, can be obtained.